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Criticizing the managers credit plan

The J.C. Nickel department store is considering adopting a new credit management policy in an attempt to reduce the number of credit customers defaulting on their payments. The credit manager has suggested that, in the future, credit should be discontinued to any customer who has twice been a week or more late with his monthly installment payment. He supports his claim by noting that past credit records show that 90% of all those defaulting on their payments were late with at least 2 monthly payments. Suppose from our own investigation we have found that 2% of all credit customers actually default on their payments, and that 45% of those who have not defaulted have had at least 2 late monthly payments. Find the probability that a customer with 2 or more late payments will actually default on his payments and, in light of this probability, criticize the manager’s credit plan.